Question

# An economist is studying the job market in Denver area neighborhoods. Let x represent the total...

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).

 x 16 33 53 28 50 25 y 2 3 5 5 9 3

Given: Σx = 205    Σy = 27    Σx2 = 8063    Σy2 = 153    Σxy = 1061 r ≈ 0.758.

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

 x = ___ y = ____ = ____ + ___ x

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

 r2 = explained % unexplained %
 (f) For a neighborhood with x = 32 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) ______ hundred jobs

c)

 X̅=ΣX/n = 34.17 Y̅=ΣY/n = 4.50 ŷ = 0.031+0.131x

e)

 coefficient of determination r2 = 0.575 explained = 57.5% unexplained= 42.5%

f)

 predicted value =0.031+0.131*32= 4.22

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